Signal sparse decomposition of redundant dictionaries is a new theory for signal representation. The theory can adaptively provide a flexible method for signal sparsity extension via using overcomplete redundant function instead of conventional orthonormal-basis function. Based on DCT redundant dictionary and Dirac dictionary,a novel adaptive redundant dictionary is presented by composed Dirac and DCT base.Combining image partition and iterative hard threshold (IHT) algorithm, experiment results show that the adaptive redundant dictionary has higher signal recovery ratio.